Don't carry slippers. Almost any place that requires you to remove shoes will have some sort of agony-inducing, undersized slippers for you to borrow. Carrying a pair of socks to put on before donning slippers in someone's house would be quite classy. Better than putting bare feet into slippers or on floors.

On that topic - Carrying a handkerchief or small hand towel is also a good idea, as many bathrooms have no towels.